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A mathematical analysis of a nonisothermal Allen–Cahn type system
Author(s) -
Vaz C.L.D.,
Boldrini J.L.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2504
Subject(s) - mathematics , allen–cahn equation , uniqueness , type (biology) , dimension (graph theory) , galerkin method , degree (music) , mathematical analysis , thermodynamics , pure mathematics , finite element method , physics , acoustics , biology , ecology
Existence of solutions for a nonisothermal Allen–Cahn type system is proved by using a semidiscrete spectral Galerkin method together with degree theory and maximum principle. Regularity and uniqueness are obtained in a special situation for domains with dimension up to two and smooth enough data. The present system may model the evolution of solidification or melting processes occurring in certain binary alloys. Copyright © 2012 John Wiley & Sons, Ltd.